Solve x+2/x+x-1/x+2=2

$$\frac { x + 2 } { x } + \frac { x - 1 } { x + 2 } = 2$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+2\right), the least common multiple of x,x+2.

$$\left(x+2\right)\left(x+2\right)+x\left(x-1\right)=2x\left(x+2\right)$$

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

$$\left(x+2\right)^{2}+x\left(x-1\right)=2x\left(x+2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$x^{2}+4x+4+x\left(x-1\right)=2x\left(x+2\right)$$

Use the distributive property to multiply x by x-1.

$$x^{2}+4x+4+x^{2}-x=2x\left(x+2\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+4x+4-x=2x\left(x+2\right)$$

Combine 4x and -x to get 3x.

$$2x^{2}+3x+4=2x\left(x+2\right)$$

Use the distributive property to multiply 2x by x+2.

$$2x^{2}+3x+4=2x^{2}+4x$$

Subtract 2x^{2} from both sides.

$$2x^{2}+3x+4-2x^{2}=4x$$

Combine 2x^{2} and -2x^{2} to get 0.

$$3x+4=4x$$

Subtract 4x from both sides.

$$3x+4-4x=0$$

Combine 3x and -4x to get -x.

$$-x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-x=-4$$

Multiply both sides by -1.

$$x=4$$